BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.6, Problem 2E
To determine

To evaluate: The value of (fg)(x) and the value of (fg)(2) if g(2) is 5 and f(5) is 12.

Expert Solution

Answer to Problem 2E

The value of (fg)(x) is f(g(x)) and the value of (fg)(2) is 12.

Explanation of Solution

The function fg is called the compositions of functions f and g and the domain of fg is set of all x in the domain of g such that g(x) is in the domain of f, that means,

(fg)(x)=f(g(x))

Thus, by above definition, the value of (fg)(x) is f(g(x)) .

Calculation:

From Section1,

(fg)(x)=f(g(x)) (1)

Substitute 2 for x in above formula,

(fg)(2)=f(g(2))

The value of g(2) is 5, substitute 5 for g(2) in above values,

(fg)(2)=f(5)

The value of f(5) is 12, substitute 12 for f(5) in above values,

(fg)(2)=12

Thus, the value of (fg)(2) is 12.

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